Fighting, as well as Reflexes and Powerhouse and melee weapon specialization, is improved by killing zombies in melee combat (either unarmed or with a weapon). Killing enemies in rapid succession provides a "Slaughter" XP boost.
The following traits reduce Fighting XP gain rate by half

An effective, but risky way to train Fighting is to travel with another character and provoke a horde, then stay back until that character loses all health (he/she crouches down and cover the head as zombies attacks, similar to the player when in the near death "Press B to Stand up" state). The attacking zombies at this point are susceptible to instant kill button combination. Eat a Snack, rush in and start stomping on their heads. When the survivor stands up, all zombies nearby will be knocked down, again ripe for instant-killing.

The description for level 7 refers to another special technique: Brute Force. This seems to be have been cut.

According to game file, each single kill gives 10 points to Fighting, Slaughter gives a bonus of 20 points.